New Researcher

Transforming Children’s Mathematical Development

Associate Professor in Education, Joanne Mulligan, is firmly convinced that children are capable of deep mathematical thinking from a young age – as early as pre-kindergarten years.

“The traditional view has been to introduce children to abstract mathematics at seven to eight years of age. Current research shows that young children develop complex mathematical knowledge and abstract reasoning much earlier than previously considered,” she said.

Leader of the Cluster for Research in Mathematics and Science Education in Macquarie’s Department of Education, Associate Professor Mulligan’s focus over the past 25 years has primarily been on the development and assessment of number concepts and processes, word problems, multiplicative reasoning, and pattern and structure with four- to nine-year olds.

She is currently principal investigator of an Australian Research Council Discovery Project (ARCDP) – Reconceptualising early mathematics learning: the fundamental role of pattern and structure. It involves implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) with Kindergarten to Grade 2 students. Four large primary schools in Brisbane and Sydney are participating.

As this project draws to a close in July, she is beginning a second ARCDP, a longitudinal study into transforming children’s mathematical and scientific development across Grades 1 to 3. The new project involves two other Macquarie academics, Dr Kerry Hodge and Dr Marina Papic, as well as Professor Lyn English from the Queensland University of Technology.

“Current research indicates that emphasising the underlying structure can significantly improve the quality and scope of mathematics and enhance cognitive development. We’ll be using an innovative, sustained approach to learning – at an optimum age – to challenge and motivate young children to develop mathematical and scientific reasoning,” explained Dr Mulligan.

Children of widely varying abilities will engage with novel patterns and structures and data modelling experiences. The project integrates research from both mathematics education and educational neuroscience and will look at how the early skills of young children can be best fostered in educational settings. Just as importantly, the study will look for more effective ways of establishing the root causes of learning difficulties in mathematics and science.

Previous and current studies by Associate Professor Mulligan and her Macquarie colleague Mike Mitchelmore have found that a lack of awareness of mathematical pattern and structure impedes mathematical development. Low achievers produce poorly organised representations lacking in structure – they do not focus on structural features when learning mathematics.

“By identifying those children who don’t see patterns early, we can predict learning difficulties in mathematics later on. Early assistance through our approach offers these children and their teachers an innovative strategy that can do much to prevent later difficulties,” said Professor Mulligan.

"In partnership with Gowrie, Dr Papic, Associate Professor Mulligan and Kate Highfield from Macquarie’s Institute of Early Childhood have recently acquired an ARC Linkage Grant to improve numeracy outcomes for young Indigenous children." The project builds on professional development Dr Papic provided early childhood educators working in Aboriginal-run childcare centres across NSW and ACT over the last four years. The project hopes to close the gap in numeracy achievement for young Indigenous children by developing culturally appropriate pedagogical content and advancing this content knowledge among early childhood educators.

In yet another partnership, Associate Professor Mulligan and Macquarie’s Dr Michael Cavanagh are leading The Enhancing Success in Mathematics project, backed by Macquarie and the NSW Department of Education and Training. The focus is tracking student achievement, improving outcomes in mathematics learning, and supporting professional development initiatives in Grades 5 to 8 in 12 schools in Sydney’s Hills District.

“It’s vital to encourage and instill in children a love of maths and not be afraid of challenges. Mathematics must be more than yet another page of sums. Encouraging children from an early age to be challenged, to think creatively and to reason scientifically will also optimise Australia’s creative and technological capacity for future innovation and new knowledge in the quantitative sciences,” said Associate Professor Mulligan.

With a first degree in educational psychology and teaching, Associate Professor Mulligan has a Master degree in mathematics and science education and child psychology and a PhD in the psychology of mathematics education. Her doctoral work was acknowledged by an award by the Mathematics Education Research Group of Australasia and was followed by a large ARC-funded longitudinal study on children’s development of number concepts and representations.

Much of her research has informed the NSW Department of Education and Training numeracy initiatives, Counting On and Count Me In Too. She also developed a Numeracy Achievement Scale for a Commonwealth-funded Numeracy Research in NSW Primary Schools’ Project.